Download Lectures 26-28

CHEMISTRY 2000
Topic #3: Thermochemistry and Electrochemistry –
What Makes Reactions Go?
Spring 2008
Dr. Susan Lait
Electrochemical Cells

An electrochemical cell consists of:



Two physically separated half-cells (one for each half-reaction),
An external circuit via which electrons generated by the oxidation
half-cell can travel to the reduction half-cell,
A salt bridge (or equivalent) to allow ions to move between the two
half-cells so that charge doesn’t build up in them. (That would stop
the flow of electrons, rendering the cell useless.)
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Electrochemical Cells

So that we don’t have to draw a picture every time we want to
describe an electrochemical cell, there is a standard notation:



With the anode (where electrons are generated) at the left, we
describe the relationships between each phase in the cell.
A single bar represents two phases in direct contact.
e.g. an electrode immersed in a solution
A double bar represents two phases indirectly connected.
e.g. two solutions connected by a salt bridge.
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Electrochemical Cells

If the overall reaction in an electrochemical cell is spontaneous, energy
is released. This energy is measured in relation to the number of
electrons involved in the reaction, giving a potential. When 1 Joule of
energy is released by an electrochemical reaction involving electrons
with 1 Coulombe of charge, the potential is 1 Volt:
1 V 1

J
C
where 1 electron has a charge of - 1.602176  10-19 C
A cell’s potential can be measured by applying an external voltage
opposing the current flow. When the external voltage has exactly the
right energy to stop the reaction but not reverse it (i.e. to make the
system be at equilibrium), that external voltage is termed the
electromotive force (emf). Since the electromotive force must be
exactly equal to the potential produced by the cell, the following terms
are often used interchangeably:



Voltage (or potential)
Electromotive force (or emf)
Electric potential difference
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Cell Potential and Gibbs Free Energy

Recall that changes to internal energy occur via heat and work.
The reaction in an electrochemical cell is a reversible process, so
we can clarify that both the heat and work are reversible.
U  q rev  w rev


Let us assume that the electrochemical cell is operating at
constant pressure and temperature (so that qrev = H and
S = H/T).
We can also divide the work into pressure-volume work (i.e.
expansion (wrev,PV = -PV)) and non-pressure-volume work
U  q rev  w rev ,PV  w rev ,non PV
U  TS  (PV )  w rev ,non PV
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Cell Potential and Gibbs Free Energy

This rearranges to give:
w rev ,non PV  U  PV  TS
When we defined enthalpy, we defined H = U + PV…
This equation is starting to look very familiar…

The maximum work that can be done on the system is rG.
Since rG < 0 for a spontaneous reaction, a spontaneous
reaction can do work on the surroundings. The maximum
amount of non-PV work that can be done on the surroundings
is equal to -rG!
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The Nernst Equation

So, the free energy change is equal to the work done on the
electrons (charge = q) as they travel through a potential
difference (cell potential = E):
w rev ,non PV  r G  qE


The charge of the electrons will be negative with a magnitude
equal to the # moles of electrons (n) multiplied by the charge of
1 mole of electrons (F = Faraday’s constant = 96485 C/mol):
Usually, we work in terms of molar free energy change.
When we divide both sides of the equation by moles of a
product (or reactant), n is converted to the stoichiometric
coefficient of the electrons in the overall redox reaction (e):
For a spontaneous reaction, rG <0 therefore E >0!!!
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The Nernst Equation

This equation can, of course, be used under standard conditions
(among others), so we can say:
and

Recall that:
r G m  r G mo  RT lnQ

Rearrangement gives us the Nernst equation:
RT
E E
lnQ
e F
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Half-cells and Standard Reduction Potentials

It’s impossible to directly measure the potential for a half-cell
since there would be no current and therefore no voltage.
Instead, cell potential is measured against an arbitrary zero
reference point, the standard hydrogen electrode (SHE):

2H(aq)
 2e  H2(g)

As it does for H, S, and G, reversing the reaction reverses
the sign of E˚; therefore, we can also say that:

H2(g)  2H(aq)
 2e

E  0V
E  0V
The standard hydrogen electrode (shown at the left) is an
electrode in which hydrogen gas is bubbled over a platinum
electrode in the presence of 1 M H+(aq).
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Half-cells and Standard Reduction Potentials

Like enthalpies, entropies and free energies, cell potentials are
additive.
o
2
e.g.
ECu
 0.340V
Cu(aq)
 2e  Cu(s)
2
/ Cu
2
Zn(s)  Zn(aq)
 2e

o
EZn
 0.763V
/ Zn 2 
As such, when a cell is constructed under standard conditions
with a standard hydrogen electrode as the anode, the measured
cell potential will be equal to the standard reduction potential
for the other half-cell.

Ag(aq)
 e  Ag(s)

H2(g)  2H(aq)
 2e
o
E Ag


/ Ag
EHo / H   0V
2
E  0.800V
Because E is measured in J/C, it DOES NOT CHANGE
when the reaction equation is multiplied by a coefficient!
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Electrochemical Cells Under Nonstandard Conditions

We can also use a hydrogen electrode (standard or nonstandard)
to measure reduction potentials of half-cells under nonstandard
conditions. To do this, we must know the exact activities of each
species so that we can determine Q and use the Nernst equation:
E E

RT
lnQ
e F
The cell below has a potential (aka emf) of -1.425 V at 25 C.
Pt( s ) H2( g ) (1.00bar ) H(aq ) ( pH  5.00) AlCl3( aq ) (0.00100M ) Al( s )
Write balanced equations for each half-cell and an overall
chemical equation.
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Electrochemical Cells Under Nonstandard Conditions

Knowing that E = -1.425 V, calculate E for the cell in the
previous example.
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Electrochemical Cells Under Nonstandard Conditions

Finally, use E for the cell to determine the standard reduction
potential of the Al3+/Al half-cell.
As noted previously, potentials can be added and subtracted
but, because they are intensive properties (do not depend on
quantity), they are never multiplied or divided by reaction
coefficients.
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Electrochemical Cells Under Nonstandard Conditions

Finally, we can use the standard potential for an electrochemical
cell to determine the standard free energy of formation for one
of the reactants/products. This is a convenient method to
measure fG for new compounds/ions.
e.g. Use the information from the previous example to
determine fG for Al3+(aq).
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Electrochemical Cells Under Nonstandard Conditions

If we can use cell potential to determine free energies then it
follows that we can use free energies to determine cell potential.
e.g. We wish to know whether the reaction described by the
cell below is spontaneous and, if so, what is its potential.
Pt( s ) S2O32(aq ) (0.0083M ), HSO4( aq ) (0.044M ), H(aq ) ( pH  1.5) Cl(aq ) (0.038M ) Cl2( g ) (0.35bar ) Pt( s )
We can look up the standard reduction potential for a Cl2/Clhalf-cell, but there is no standard reduction potential listed for
a S2O32-/HSO4- half-cell. We can, however, look up standard free
energies of formation for each species in the reaction…
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Electrochemical Cells Under Nonstandard Conditions
So, we’ll start by calculating the standard free energy change for
this reaction…
kJ
mol
kJ
 fG(H 2O( l ) )  237.1
mol
kJ
 fG(HSO4( aq ) )  755.7
mol
kJ
 fG(Cl(aq ) )  131.2
mol16
 fG(S2O32(aq ) )  522.5
Electrochemical Cells Under Nonstandard Conditions
At this point, we can take one of two paths:


Calculate the standard potential for the cell (E) then use the Nernst
equation to find E.
Calculate the free energy change under the actual conditions then
use G=eFE to find E.
Either way, we get the same answer and, either way, we need to
find Q to get from standard conditions to actual conditions.
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Electrochemical Cells Under Nonstandard Conditions
Finally, we calculate E. Is this reaction spontaneous?
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Using Electrochemistry to Measure Ksp Values


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Ksp values for relatively insoluble solids are tiny.
e.g. Iron(III) hydroxide has a Ksp of 410-38. That means that,
at pH 7, you could dissolve 4 fg of Fe(OH)3 in 1 L water.
To analyze a solution this dilute, we can’t just titrate!
We can, however, measure the Ksp of an ionic solid electrochemically if we can find half-reactions that add up to the desired
solubility equilibrium expression. Often, this means that one of
the electrodes will consist of the ionic solid coated on the
corresponding metal.
Once we have constructed the electrochemical cell, we can:



Measure the cell potential (E)
Use the cell potential to find the standard free energy change (rG)
Use the standard free energy change to find the equilibrium constant
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(Ksp)
Using Electrochemistry to Measure Ksp Values

Let’s say that we can’t find the Ksp value for silver(I) iodide:
We can obtain this net reaction using a Ag/Ag+ anode and a AgI
cathode:
The value for the electron coefficient (e) is _______ and the
standard cell potential (E) is _____________.
o
E Ag
 0.7991V

/ Ag
o
E AgI
 0.1518V20
Using Electrochemistry to Measure Ksp Values
This allows us to calculate the Ksp for AgI:
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Batteries

Electrochemical cells produce a voltage, so they can be used to
power electrical devices. The voltage produced depends on:



Standard cell potential (due to half-cells)
Concentrations of reactants and products (Q in Nernst equation)
Temperature (T in Nernst equation)
The voltage does not depend on the size of the cell – that just
determines the quantity of available reactants (i.e. how long the
cell can run before the concentration of reactants is too low for
the reaction to be spontaneous).

Typical cell potentials are ~1V. If we want/need a larger
potential, we must connect multiple cells in series, producing a
battery:
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Batteries


In theory, any battery can be recharged – just apply an external
potential to force the reverse reaction to occur, “pushing the
electrons backwards”.
In practice, this isn’t always easy (or safe!)

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In some batteries, the electrodes can be damaged during discharge
In some batteries, the electrodes get coated with resistive products
which cause heating when current is passed through them.
In some batteries, the desired “reverse reaction” is not the one that
occurs when recharging is attempted – generally because there is
something else that is more easily oxidized or reduced. A common
example is the electrolysis of water – used to make pastes in many
batteries.
A reliable battery is a good battery. Many batteries contain a
paste so that the solutes are always saturated in the small
amount of water available. This keeps the solute concentration
constant – thereby keeping Q and E constant.
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Alkaline Batteries

An alkaline battery has a zinc anode and a manganese(IV) oxide
cathode. As the name implies, it operates under basic
conditions:
(+)
Cathode(+): paste containing
MnO2, graphite, and water
Outer steel jacket
Plastic sleeve
Anode(-): Paste containing
powdered zinc, KOH, and water
Inner steel jacket
Brass collector
(-)
Cell base
Because there are no solutes in the overall reaction equation,
Q ≈ 1 and E ≈ E, giving a constant voltage.
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Lead-Acid Batteries

An lead-acid battery has a lead anode and a lead(IV) oxide
cathode. As the name implies, it operates under acidic
conditions (HSO4-(aq)):
The cell potential is ~2 V. To get a 12 V car battery, six cells are
connected in series.
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Fuel Cells


We know that burning a fuel releases energy as heat. This
energy is more efficiently harnessed if it is produced by oxidizing
the fuel electrochemically – as in a fuel cell. It also causes less
pollution!
A lot of research is currently being done to develop a practical
hydrogen fuel cell – which would be a very environmentally
friendly power source as the only waste product would be water:
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Fuel Cells


Since fuel cells always involved oxidation of a fuel (hydrogen,
methane, methanol, etc.), the reaction at the cathode is always
the same: reduction of oxygen to either water or hydroxide:
What is the reaction at the anode in a hydrogen fuel cell?
Assume basic conditions.

The major difference between a battery and a fuel cell is that the
reactions in a fuel cell cannot be reversed, so it cannot be
recharged. Instead, the fuel must be replenished
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Membrane Potential


Biological membranes have transport systems that facilitate the
movement of some species more than others. For example,
they tend to be relatively permeable to K+ but relatively
impermeable to Na+ and Cl-.
Cells use energy to maintain a high internal concentration of K+
but, due to the permeable nature of cell membranes, some K+
will always leak out:
The free energy change associated with this process is:
Because the internal concentration of K+ is maintained to be
higher than the external concentration of K+, this process has a
negative Gm and is therefore spontaneous.
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Membrane Potential

Since the K+ ions are charged, an electochemical potential is
established, and we get a relationship similar to the Nernst
equation:
where z is the charge of the ion (+1 for K+)

As K+ travels through the membrane without the accompaniment
of any anions to balance its charge, a charge imbalance builds up
across the cell membrane. This generates an opposing potential
called the transmembrane potential ():
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Membrane Potential

The transmembrane potential of most cells stays relatively
constant. For example, [K+] inside a mammalian muscle cell is
155 mmol/L while [K+] outside the cell is 4 mmol/L, giving a
transmembrane potential of -94 mV at 37 C (calculated using
the formula on the previous page).

Neurons are an important exception to this rule. They transmit
information by means of changes in the transmembrane
potential. The transmembrane potential is normally about
-90 mV for K+ (as for the muscle cell above); however, an
external stimulus can cause ion channels to open, allowing
some Na+ ions into the neuron and some K+ ions out. This
increase in membrane permeability to those ions alters the
transmembrane potential which can travel along the neuron
until it reaches a synapse – where it stimulates the emission of
neurotransmitters which stimulate opening of ion channels in
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the next neuron.